{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.09-Principal-Component-Analysis.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  In Depth: Principal Component Analysis\n",
    "\n",
    "# 深入：主成分分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n",
    "Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n",
    "\n",
    "目前位置我们只是深入了解了有监督学习评估器：这些评估器构建在标记的训练数据的基础之上。下面我们看一些无监督学习评估器，它们能在没有已知标签的情况下聚焦在数据的有趣的特征上。\n",
    "\n",
    "> In this section, we explore what is perhaps one of the most broadly used of unsupervised algorithms, principal component analysis (PCA).\n",
    "PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, for noise filtering, for feature extraction and engineering, and much more.\n",
    "After a brief conceptual discussion of the PCA algorithm, we will see a couple examples of these further applications.\n",
    "\n",
    "本节中，我们将探索一个可能是最广泛使用的无监督学习算法，主成分分析（PCA）。PCA本质上是一个降维算法，但是它也可以作为可视化、过滤噪音、特征提取和特征工程等方面的有用工具。简短的对PCA算法概念进行介绍之后，我们会看到更多应用的一些场景。\n",
    "\n",
    "> We begin with the standard imports:\n",
    "\n",
    "首先导入需要的包："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducing Principal Component Analysis\n",
    "\n",
    "## 主成分分析简介\n",
    "\n",
    "> Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n",
    "Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n",
    "Consider the following 200 points:\n",
    "\n",
    "主成分分析是一个快速而灵活的无监督学习算法，主要用于降低数据的维度，我们在[Scikit-Learn简介](05.02-Introducing-Scikit-Learn.ipynb)中已经简短地介绍过它。在二维数据集中更方便我们理解PCA方法。例如下面200个数据点："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> By eye, it is clear that there is a nearly linear relationship between the x and y variables.\n",
    "This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the y values from the x values, the unsupervised learning problem attempts to learn about the *relationship* between the x and y values.\n",
    "\n",
    "仅凭眼睛就能清晰观察到x和y变量之间的线性关系。这种数据线性关系让我们想起在[深入：线性回归](05.06-Linear-Regression.ipynb)中介绍的内容，但是这里的问题有一点不同：我们不是希望训练一个可以通过x值预测y值的模型，而是希望模型能够学习到x和y值之间的*关联*。\n",
    "\n",
    "> In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n",
    "Using Scikit-Learn's ``PCA`` estimator, we can compute this as follows:\n",
    "\n",
    "在主成分分析中，这种关联关系被量化成在数据中找到一个*主要特征轴*的列表，然后使用这些轴来描绘数据集。使用Scikit-Learn的`PCA`评估器，我们可以如下计算："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The fit learns some quantities from the data, most importantly the \"components\" and \"explained variance\":\n",
    "\n",
    "拟合过程从数据中学习到了一些量值，最重要的是其中的“成分”和“可解释方差”："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.94446029 -0.32862557]\n",
      " [-0.32862557  0.94446029]]\n"
     ]
    }
   ],
   "source": [
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7625315 0.0184779]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> To see what these numbers mean, let's visualize them as vectors over the input data, using the \"components\" to define the direction of the vector, and the \"explained variance\" to define the squared-length of the vector:\n",
    "\n",
    "要查看这些数值代表的含义，我们来将它们可视化成输入数据上的矢量，使用“成分”来确定矢量的方向，“可解释方差”用来确定矢量的长度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    linewidth=2,\n",
    "                    shrinkA=0, shrinkB=0)\n",
    "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
    "\n",
    "# plot data\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> These vectors represent the *principal axes* of the data, and the length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n",
    "The projection of each data point onto the principal axes are the \"principal components\" of the data.\n",
    "\n",
    "这些矢量代表着数据的*主要特征轴*，而矢量的长度代表着这个轴对于数据的分布起到了*多重要*的作用，更精确来说，这是数据被投射到这个轴上时方差的度量。将每个数据点投射到主要特征轴上被称为数据的“主要成分”。\n",
    "\n",
    "> If we plot these principal components beside the original data, we see the plots shown here:\n",
    "\n",
    "如果我们将主要成分画在原始数据旁边，会得到下图："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](figures/05.09-PCA-rotation.png)\n",
    "[附录中生成图像的代码](06.00-Figure-Code.ipynb#Principal-Components-Rotation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> This transformation from data axes to principal axes is an *affine transformation*, which basically means it is composed of a translation, rotation, and uniform scaling.\n",
    "\n",
    "这种将数据轴变换成主要特征轴的方法被称为*仿射变换*，基本上表示这可以通过转换、旋转和统一比例完成。\n",
    "\n",
    "> While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration.\n",
    "\n",
    "虽然这个查找主成分的算法看起来就像数学理论而已，但是实际上它在机器学习和数据挖掘领域有着非常广泛的应用。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA as dimensionality reduction\n",
    "\n",
    "### 使用PCA降维\n",
    "\n",
    "> Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n",
    "\n",
    "使用PCA降维主要包括将一个或多个次要成分从数据中移除，从而获得数据的一个低维度的映射并保留了最大的数据差异。\n",
    "\n",
    "> Here is an example of using PCA as a dimensionality reduction transform:\n",
    "\n",
    "下面是一个使用PCA进行降维转换的例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original shape:    (200, 2)\n",
      "transformed shape: (200, 1)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "X_pca = pca.transform(X)\n",
    "print(\"original shape:   \", X.shape)\n",
    "print(\"transformed shape:\", X_pca.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The transformed data has been reduced to a single dimension.\n",
    "To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data:\n",
    "\n",
    "转换后的数据被减成了一维。要理解降维的效果，我们可以将数据进行逆转换并将它们沿着原始数据的方向绘制在图中："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NK87VD2ol6GT2rFZjXyPSDfR73s2lg2/n8mwViFcSv0k6/x0hQUCIPWArC7e28l60MoJ6CTbtbKB0q0hcyjSwTI1aI6Dph4wsvUTlP/4Nw/OX1m6MBmga3rN/S/qhjxM88XkiN+7YI3S01pxAoFtEhk1YOET91ndw7A0/yz0wsIfJJJkEASH2gI3SL7fzXnXXZ3apwULZZWqmylDe6inYtLOBxofSXLpWYWhRcWTy70i7c2iE6JoWV25YTxTFwz9eI67d8+BvsPTdL2HVZ0DTqKWKXD7+TurjDqWaz9EDOW45ImP8gyRBQCRSP8ff+6Hd4YZhxFypQcP1MQyd4nBmy+9lWwZ11+fStUpcjjmfolL3aHh+p3QzrB1sJsayTP39v+fQle9wNHrtgS4RerxStxUA1krr1KBVzTMEKw2Adfw0Sw+eoFxrUql7LNU8XDfAWHQZLaS3NPwltkeCgEicfo6/93q81QJO93YNmCs1qDY8smkD09CpuT7Vhk+l7m2qXd2LwGaXGvFiKiLGhzNoWoNGM2Cu1OCmYpzaufLxh41//Bres39L1KxxeJX31zaT1tkq3WDd+87OpnzW4rlX58ilLUZyJnVTp9rwcE6M7GgA2GuBf6+QICASp5/j7yu1O5rJuRqlpTp11+fKfI1CxuTgaLbzLN6JsWynHe1AVKq6WIaB70M6pXPy0BCGoW26Xd2LwBbKLqP5FOPDGbJpE0hzaaZMuRYSRVFngdWR6FWq//E/E85f3PD94bUrf23dvYBUBuved5K+/5++9hnVPE4cKnTWHqRtkwMjaSo1j4nRnk8zfq8eO/ZBB/79RIKASJx+jL+v1vkAnY4mrWtMXiszV2pwcDiDrutcnqty9EAeO2WgLiwyMZ5ZFohM0yCXNjk28VoxsiiKtjQv0F4EVnd9ZhZrvHq1jOsGpFM6uqZh6hr+xWcpnv0GVvkqEC67vu911W4ERJoJURAXdgMiI0Xl5odoOI+sWr6h5voM51KM5O1tnedmOvadDPz7nQQBkTgblT/YyFqdj65pnY5mdrFBNm2yWI6HdQq5uMJmO71ysepybCK37H3zGYtKbfnD1Fe2a2XwyWfjn1ntSrhS96i5HouVJtWGh2Xo1NyQXMbidPUHHLz0LQgDVuq9PKMGmo6vp2DkKI3bHiLvvJmFxSpRFFFbo1Pf7ufftpmOvZ8T7zcaCQIicTZbOG2ltTqfC1fKnDoWdz51N+50s2mdWiPuaJalV+bsZRPBSxWXhYpLvRFfrR8czWKay8syrAw+S5Um//jSDENZE0PXMQ2N2aUGd988Rj5jMT1fYzhvk3/575i49iRWuPyJX+0ibCu39UQzCAoTVO94D883j3LicKHnTn27n3/bZjr2fgWeG5F8AiJxusfMZ5ZcGg2fjG108uh7ebziap0P0PXQdIuFRpOsnaLuNmj6AURg6OA2A5wTI1y4WmJ2qYGhw2LZJQgjxgo2rhdydioe1minS56dWuL5CwvUGz4pUyOMos4Vvu+nOXm4gOdHXJ6tUqq4HDqQ48pslTtLTzJ09Yl1J3M3M/TjpYZx3/AhvIm7gbj09BEv7sQhHtZxvWDdTr2XwnW9jPVvpmPvV+C5EUkQEImUz1gwlqXa8BjOZTodw2Yer7iy8zlyINfpDA+MpJmajjudUzcNU657lKtNbjky3Cl7MLNQJ5PymF6oY1smh4fTGLqGoWsUjwzheWFct+fyEinLYHq+gm2ZTC+4jBZsri3UKGQsFsoNDo3HQ0vZ+Re4Y+HbDAfzHItorcpde/q2lwBQTR3kzF2/xetPFTt3QamuSeV2oJqer1GqNTF1fcNCbusVrut1rH8zHftmK6YmiQQBkVhbnSxcq/Pp7gyDMOL4wXiCNwJGC+nrrmaj1ntNL9QIwjg7aCiXwvMhCMJO0bahXIrZxQZNP8TzPWzLwA8jDFOnWDvLWxvfIjdbXtHV62ia1tq2tYcwRWict+/g+8Pv5kClibqwiHNihErNW7UjzR8d7ssDVnr9vWy2Y++1YmrSSBAQibXVycKNOp9eO0MNOH+1jGkYQETd9bk8V6WQTjFfbjCUSRGEkE3rhFHEaN5m8mqZ8eEMb7j6XzjZfAFttYF9AEI0zVyz/19tgZdvj/Ly0V/iH0sH0QwNtxlQd30mLIMgDFmoNJier+14WuVmfi/SsW+fBAGRWNuZLNxu51Ope1yZrXJ1rkbaNmi4cYcbRiG6oVGpeWRSJpap4/kRKctgZOks93tPUrxyGYNWVs96ifphQLu7X2u3SLfwR0/SuO0hXtVP0HAD7EaFQtak5vrk0ha6DpquEYQhdsrY8bRKmcQdLPlUxQ1hK6tBd2OysFOf//ISsyUXy9BYKrnMl12GchYjQxkMTePERIEIOHz5Wxy5+kRcpmHTIkIMNKK4ekPU9R6ajnbiTZy/9QPxGL+pU55cxNBhbCiF6/k03IC0rVN3A9KWQTplDiStUiZxB0uCgNj3troadNCThZ36/Et1bMug0fCoAxOjGULAMGBiJMPtk/+JsXM/6csxdS0iNLNcveuDHD79lmVrCKbna7ilBtNzdRp+QLnqMlZIM5RN4YcWpYrP9HwN09AZzqewLWNLV+SbDdAyiTtYEgTEvred1aBbGdbZag2aTn3+MB73HhtOs1BqMLvU4GD9LG+t/i256cam2rKeSDMIcgep3/1ewrE7Op9Hd9DMZUxmluoYOtx+bIRri3XK9SZhGKHpYKcMxocyRFFIudZkqeJy18neyztvJ0DLWP9gSBAQ+94gV4Ou16kBneBwtOaRag3Et7ddma1ytJgjnTK4thBw3D/PWxe/Sd6bQd9iBs9qPHuU+ut+Bf/Q3Z1tqa6yDN1B89JinWzaREOj0Qy4+fAQV+drTF6tMJxPMT6chijCTplkbYOsbW3qilzKNex9EgTEvtfvicT1rvTX6tTOXykRRlEnOHh+yCtTC0SRxkghRT5jYlk6F6bL3Ln0fe658Hfo2zzvbr5mEzzw6xTvejNnp5bwwxC76/Xuz6M7aDZcv/XUMKg1AjK2yclDBco1j3tvGes8TQy2Vt9HyjXsfRIExL7Xz4nEjYYv1urULlwpLyudkE6ZVBs+RBETYxnSLz7OG175JnrorXbYLQvsUcwHHmXstvs62/JZi2deniUMI/IZk0I2ha5rnc+jO2i2nxqmoZFOxW3vLmux3cAqmT57X99+E47j3A58ARgH5oCPKqVeXrGPAXwaeBdxmvIfKaU+3682iGTa7kRi95X/hStlFquNuAPNWpw8NESuVYcnf3R4zU4NXisd0Zabf5ETF75O5qml/p1si6fZ1G5+kJrzrnihWuuZA+1zmRjLUK55rSJyPq8/Vex8Ht1Bc6xgc/5qvJ7hxEShU/LBOTESl9Fge4FVMn32vn6G488Bn1VKPeY4zkeAPwUeWrHPrwK3AaeIg8WPHcf5plLqfB/bIW4gvU7CbnUisfvKv+n5vHhxHtuKC7h5fsiZs3Pce8sYKSv+p7JWp3bkQI6mHzL2k8ewLz8NRNyxrTNfLgKWyPOE+SDmsXsYyae56+axzpBPO0h1D1e1SzW7XrCsVn930Gx6YWdlcxixrORDLm1tO0NHMn32vr4EAcdxDgL3Ab/Y2vQl4DOO4xSVUjNdu34Q+DOlVAjMOI7zVeADwB/3ox3ixjKIB4F0d5o/nS5TyMRDJ3U3YKwQd6JnL5e4//aDwNqdWjT1LMHf/in6ikqd2xGg8f/pb+Ip6434YUTaMsimLQ6bBkOt0tSwfIy91zH4XoJmvzJ0JNNnb+vXncAxYEopFQAopQLHcS63tncHgePAha7vJ1v79Gx8fH/fRhaLhY13usFs9ZznL8wzUSyQTnU9+rDp04y2/zmWa00uz1S4MFNlfNimUMgQRBpHJwrMLzXwo5Bs1sa0DOZKLnfffpBCNu5407Um3qVnGfnRlzGr1wijePVuXPxh6yLAPniCzM99iG+cz/OTV66RMnX0ZkjO1hjK2vEK4kjjluNj5NJW5zMZHtYpFgscrXl4fnjdZ9Z+fRDkb3x/2XezM3NzFcKwf+l0g9SP4lr7zXbOeepqiXzGpF67PkNlLLv6IwQ3GjrqXrFbyKUIg4iZuRrX5qqEfkA1CEiZGn4D5hdrhFHISDbFT1+6Rs31ycy+wNizf4kZ1DBWHL/nv8qVO2rwqn0nS697lLe9/ggRkLtymZGMxUK1ianp5FImlgHlapMgCFHnZpY9c+CWI8PMzJRJaXBpptxZBdxd3G4Qf3vyN7736Lq27sVzv4LAReCo4zhG6y7AAI60tnebBE4AP2p9v/LOQIiOlZOwddfn6nwNzwtXfYrWRkNH3St2h3Ip0Fp3Fl78oJdq3adcb5LPmNx8aIgIjYVKg1ML32NcfZ+i32B71/rX//h8mONrxY+hofGzttFpZ931ODYxxEi9ia5pNLyApuczNmxz14lRSjVv2TMHOsXrZAxebFJfgoBS6prjOM8AHwYea/3/xyvmAwC+DHzMcZyvEE8M/zLwtn60Qdx4uidhgyDk/NUybjOkkDF56eIiz5+f59BYlrRtslByGcpb6y5K6l6xm03rgEbKCpkvNcjYFqahcfPhAgulJkde+iuOVJ7b+EHqmxABJS3Pt4y3M2meRDc0fD8k54eMDaUZG0p32jkxlmVmoc6omabW8JheqBKEcGQ8z0K5STplcHyiQMY2r+vgZQxebEY/h4M+DnzBcZxPAgvARwEcx/kG8Eml1FPAF4GfAdqpo59SSp3rYxvEDaT7qvbClTI6GilLw7IMdD3k2mKNxarL/bcXqTY8Gp7feqpX/Ge9ckK05vroGpSqHtdaK2Xdpo9h6BwczTCydJGbpr+PMfcqOv6q5ZY3KwRqqYOcO/QLPFOdwDA0lioeTdenYFuM5W3qzYADw+nOw+rbD2K3LYO5UvzkseF8mqbnk8tYWKaG50dcW6zRDCJu3WYbRbL1LQgopV4k7uBXbn9319cB8Jv9Oqa48bWvaufKLhevlnG9AM+PaHoB+bRFwwuYL7sUshaNZsBcqcFNxXj8c+WiJLfp88KFBVzPZ7HSxDIM7lh6kjdGP8F6tX9ZPRE6Xn6CySO/wHntBOPDGUxDY/hyCcOIM48M3SJjGXhBwGje5s13Hepc0beHwTK22TmX+VKTlKljtdYixIFAp9GQlbdie/bdxLBInkrdY6FUp+p6DOcsgiBiZrHO2JBN1jZouD5HDuS5NFOmXAuJuh592P2Q9stzNSqNJiOLL/OQ+yTjzPd1uKduDHPp5vdSG7+DQNOYnFrCD5pcnq0ynLcZG7LRNI2sbZJPW3hhhK7B7cdGqdQ8ri3Mxa9lresWauk6ZFIWTT/AMnS8ICSMIjQt4uzU0nWT4VstcieSR4KA2PPaY+TzJZdGM65tbxo6C2WXW48Ok7ZNsmmTgyNZStXrH31YqXtc+Lu/5IHp72BFPTyMpQfdD/Rq2qO8fPjdGMfuJWtbVMsuF6fLNIOQkVwKy9KZW6pjGBqnjo6QsU0iWNbhd09ot8+3+zGOdxwfxQ/D1qSxT9o2SacMlioefhgumwyfGMte9579Xl8hbhwSBMSe1x4jd46PoCYXqDR8LFNjeqZBpepRyKe4PFtjOJfi9acOMDGa7fxs+YdfITzzdY4RbWmAf+W8QARcG74X/y3/IwBzpQblmkfOtrj35Dj5jMXZqSV0Q+PqbJUwDCnkUkyMZbFMnbGhNLd2TdqenVpatSBdpeYt26+d2VQcyXTuDs5fKTExmr3uZ9WFRSbGM1K5U/REgoDY89rP4g2CkIOjWcrVJldmqxSyKUxDw/MDrsxVODhygOn5Gtm5F+EH/w7qJdZ8BO8Gun9OA0I0vNwhFk/9EguF2xjWNVKmTj5jUa17pNNmPIQzlqXmxpPNRw5kO+8SRRE116fmLh/D38wK35Wpn6NDGYbzqet+drHqcmwit+F7CgESBMQArByfzmctKjWvp+814qvteus1tIip2Qr5jImu6wRhRMY2eOvVL3HwR/GylDU7/u7L+qhr22q76ibWG95D+v5/umz7ga7zmV1sMF92mRjNMpxPdYZddE3DMnWqbnzHAuAFIaahX1c9czNVNq9L/ZxaWvVn+1UBVCSD/FWIbUBL6+UAABdkSURBVNloArJcay5bxLVUafLcq3OcOFRgOJdiqdr6fqLAcD513evnr5apuz6HxrLUGj6NZkCjGfBLla9wJLy0+QZ3B4JVAkCASWP4BPn7f4l0V3nmbt2d8VA+RRhGTM1WabTuAPJpi8JQmmtz1U7gqjWWp4G2P7u663PuSolCxly2AriXKptrFbPrVwVQkQwSBMSW9bJK9/JMZdmYd6XuYRo65y4vMZRNUao1sS2TSt1jpGBTqXvk0vFk7kjeJgjiK9iFkottG5x45a94U+nZ7Wf1rHiDmjHMxZPvoTJ2B8XhDIdv2fgRijXXx9BhaqaKZelkbBMvCLgyX+MNdx3Cd30uz1YBOH6wwMnDQ6uucL7t6BDTC/VVVwCvZ73Vwf2oACqSQYKA2LJeHh1YqXvL6uyXqk1KVZcwgolRk2sLNZrNOGPnJqDRDMjYOvXW2HnaNrGuPsfxC18nF/ZWn0Vb8fWy+eAVY0W+bnPJ+RDXMrdx203DHNjE07OytsnktTKWpZMyjdbxdAoZk1K1yT23jHPPGsFk2WdnGUyMahBFXJ6txovdekzpXGt1sKwaFr2SIJAQO5E33sukZj5jMTlfpVL3aDQDrs7V0PX4kYuappHNpKjVPdxmq9NPGdTdIE6BfPFx7j3792hBc9NtWzMRSIOyNsSTmf8O9+CdneyatB5Hhs2MnU+MZfnpq3Otss5RvIjNDzgynqNS91YtctfW/dnVGj5TsxUsQ0fTI/xQUjrF4EgQSICdqsvfy6TmUC7FhekypqHjegFzlQaNhk8hOwpEZG2TxXKDXNoiiiLyGYto6jnuvPY4lruwpXatDAARMF24h6eK72HqWgXbNhjNp9E1jYvXyowPpTl100jnqVq9jp23h2NmFmvUGgHplMHRA3kMQ9vwc+3+7OZLDVKmQURExjYlpVMMlASBBOhl2GYt691B9PLowFK1ycRYhlcvlwgjGC/YBDmba4sN0ukUw1mLO46P0vQi/IvPcvzsNzArVyEKt3XOETrlwgmmDvwcT1cPoWtgNUMOHciRMuMyy+Wax9EDOQxNv+6pWr06eXio84D5ZU8aK+ZpVNcuRdH92dVdH8vS8Lyos8ZBUjrFoEgQSIBec9FX2ugOopeyxZW6h+dHHG51vo1mwMxCjeGll3nDy98l7c4CoKeHIAqgWQdNvy4I9LLOKwLKVpGrJ97Fee0El2YqpGsGWhQRRhrNpofnaWgZODSWpTiS4WgxR6Xuc28PE8GrWeszKGRT6waB7p+LIogijZsO5jrF7ySlUwyK/JUlwGZy0bv1cgex0QRku2zDUNaiOPn3FC/9N3SWd/CabkJtHtBA00CP29XrAt9QM7h66O1cPPwgnh+yUHZJWxCEAURGp0ZP2jJp+h71RkDTDzh6IN+Xznark7Dtn2vfFei6tmrdIyF2kgSBBOhl2AauH/qZK7sUh+1l+2x2mOJIMY+uweEX/j0HFs9c97oGEK4Y+olColXuBjovGykqNz/E1OEHydoWr14pUXcDcn5EpdLE8wNMQyNtWYRRiKZpDOdS6LrOUtVltKBxZDyHYWh7orOVB8GI3SRBIAF6HbZZOfSzUKqTMjRGCq8Fgs1eOReyKe7LT2OvEgCgnbEZLvsuIiLSdLQoon0/EOgWVyd+nsybfrnzs8NegOeFTIxlmF1qkE3rLJYiml5IuVqPH87eCgCuHzKaT3HsYB4djaobMJ7aO52tpHSK3SJBICE26mRWG/qJq1HWyaTNnlaeepNncP/hr4iWpgHQhw+Rffij5M59i4C1h3ciQNOMeE5AN/GtAkazBJqGnztE/e738nzzKGhwquvnUqbOhStlThwuUMimmCs1CMMI1wsYH05zaDzLlbkatYZPytQYylmEkcnB0Qy6pkl5ZSGQILDn7FYd+NUmj4dzKTwvxNT1Ne8gyq88TfMnj6OXr6B7dfQoBD0OJOHCZWa//lmCMAS01jX+6iJAszLohQPo9SreyAncU+/Am7gbgOD8AqV6k1cuLZK2TcaH0rjNgNmlBpoGGdtkbCiNeyCI55WJA9mB4TSvlBcxDYu0bTA+lCZjm7heICmYQiBBYE/ZqXz+Xqw1ebyy9LE3eYZK+2o/CAg1DT2VR/ebaFEQd+ZRBIYBUUTg1uKJXjsHbmXVY0doeNmDDP/8h7GOn6ZS95hsfQ6pKGKp0qTUWnlsGjp+EPDihQX8IGRsyMayNIIwLizX9COKIxmqjbguTy5jceLQEHbK6DylC66f25CHsIikkiCwh2wnn3+7epk8bvzj1/Ce/hpR14StFoHRXF7OIYpCNAxAgzAA00az0vFdQFcgiNCp3/5Olm59GFPXOdCVcdQ9h1Gqetx+bJiUGS+sajTjR0wO5VKcOFTg0rUKlhURBhGXpitYpsaJQwWOHIhTLj0viLOOunTPbexm8BVit0kQ2EO2ms/fDxtNHnuTZ/Ce+etlAaAj6i7L+dpkLkSgGxhjN2GdfgTvzOMES9eop0ao3fIQ0ZF71pxn6J7DePbcHPmMGZeZSMf7vXxxEVrDQDcdzPPqlRKvXFrC80MODNs0mgEXr1U4OJohm06hafFcwWoBbjeDrxC7TYLAHrLVfP5+yWcs7OACzae/TLh0lQioDE9gv/lX8M48ThQEXXuvKM6vtYrEtQNCGEIUYWQLWKcfwTp+Guv4aQBqCzUmLyyyeG6ekZyNc2Jk3Svu1T4X09A6V/d11+fC1TJoEaN5m7GhNKVqk6xtUqp43OcUAdYMcLsZfIXYbRIE9pBe8/l3gjd5huY/fJlw4VKrI9dB14kWrtB44vOgQaSbaKHHank+kWYSWhn0ZgU9ikDT0EcOc+Dhj1Ibei2npz32PjGe4dhErvNM3VzaWjMQrPa5tK/uFysuL04u4LWCRDZtUnP91gSwwUjB7rzvWlf1ux18hdhN2/4rdxwnC/xb4H7AB35HKfXXq+z3IPAN4KXWJlcp9TPbPf6NZNCLhrzJM/EQzfwl8Brx4qzO0E6c0YOuxa8ZcSdvuF7r9dcCQaQZhGaKMH8Q83W/RqHrYSy5YoHazGtzBlsZelntc7n75jEAnlYzNNyAfMYikzbJ2iZ+EFFteARhxGghfo7vehO+uxl8hdht/bjU+R2grJS6zXGcU8B3Hce5TSm1WirI80qpN/bhmDesQS0a8ibP4D75xThzx2/GASBsD/e0hnqiEDSzlb9vY5oWPkPobgWNeF8/PYr1c48yvMZTuFba6tDLWp/L6JDNKX2EWsNjsexSdX3qDY+lqsdo3iaXMZmwsutO+MqKXZFk/QgCHwR+DUAp9bLjOE8BjwBf7sN77yk3Uhqhd+Zx0E00yyYK/daYfsiyoZ72il3ttcndxo//hqA0g5sew73tHYze8cZ1P4NyrbnsSlyDvg69ZG2TIAxpuD6ZtMXlmTJNPyKdMhgdSlGpexTDCE3T1r3rkBW7Iqn6EQSOAxe6vp8Ejq2x7+2O4zwNeMC/UUp9YbMHGx/fnVv0cq3Jhdka+UKa8TEjro1f9ThwIK4Y2atisbCDrYxVzz7N/N8/hj9/mQiwxo8w9tBHyN362tX6ZHUOM51H0zQ804onfQ0DAp9lD+GNIvR0hgNve1/88/c/0HM7yrUm6sLCss/Mi1wiLSKTtbGteJvWDHBOjG7qc2xL52zUhQWGhzKoC/OMj+RIWQZ33zrO7GIdy9BphhpHRnIARFFEqdYcyO9hEMfYi5J43vv5nDcMAq1O+/gaL09s4lhPA8eUUkuO49wMfNNxnCml1Dc38R7MzVUIw17rS/bP2akl/DAk8g3qrW2uF/DTl64tW0y1nmKxwMxMb49I3Cpv8kw8ketWO9kz3swlpr/2GdJv//VOhk6UGyeoLsZ3AvYQVOeJUzrN+P9hnFuvjRwm9eZfoTZ0atnYftt6d0dnp5bIF9LUa27nM9OiAK8ZUqHBta6faVTddUsvr2c8Fz9Pt9kMODSW4cBwGpMIv+nTCEL8IGQ4E98FuF6Aqes7/nsYxO96L0riee/1c9Z1bd2L5w2DgFJq3cFex3EmgRPATGvTceBbq7xPqevrVx3H+SrwALCpILBb9ksaoXfm8XgiV9eWp20263hnHu8EAev0I7hPfpHIAy2VIQoK8UKuVAZj9GgnrXM9Gy2yqrk+42OvBU1oTbx6Yc+BsxfdQzl++NpQ09hQmvNXS2RsU0o0C7GGfgwHfRn4F8BTrYnhNwEfXrmT4ziHgatKqchxnDHgYeB/78PxB2Kn0gj7Pc8QlmfiiVxN79oar9wNyzOdLXEH/yjemccJyzMYI4fiwFC8kyvt9kwtrduejTJ9sq0aPd12MvVyZZaPYWiMD2XIpU2Z8BViDf341/jHwL9zHOcVIAD+J6VUGcBxnE8Bl5VSnwPeD/ym4zhe67h/rpT6Wh+OPxA7kUa4E+UK9EKRoFaik+IJtFfu6oXisn27F3Ct1p6lSpNXppYYK8QLsFYGhI3ujibGssxVvTVX6vbbWqmk0ukLsTYtigY/vr5FJ4FXd2tOALZ/1b5y7LA9z9B9d9Ees24Pl7Rz+cPyDHqhuOEwzWpzAkQRpPPL5gRW092eWsNnaraChoadMjg4msFtBssCVC/tT+dsfvrStRsio2oz9vo48U5J4nnv9XPumhO4GTi/8nVZErkJ/U4j3OhKelkufypHWF2Mv+fRNTtz6/hpePA34rr+i3Hph2buIPU738to8U7W63672zNfapAyDUxDo+76q6ZX9nJ3VMim+jr+L4ToLwkCu6h7nsGa/inpV/4bem2Ooew4nvmeZbn8AFg2kceyCd7VWMdP4xbv5NV2OeZWB72wwVBTd3sazYBs2qDph6RbY/grJ8JlkZUQ+58EgV3UvpK2rz1P7oWvEGoGgZHB9sqtzJ0GWm5s+Q+ZqWUTvGvZSnmG7it729KpNQKiKGJiNAusPqkri6yE2N8kCAxQ9ezT1L7zlc74vn36EW45cifuM08QYKCZNraho+sWkefGufp+E6yuh737zesmeFezlZTW7it727aouXUmxrKkU/GiLkmvFOLGI0FgQLzJM8z98C8II33Z+L79wKPQXIBMDq37wSdmCgwTQp/Ia33vNyH0sU4/suHxtprS2r6yv5XXJsJlqEeIG5cEgQHxzjyOZphoWqsT7Rrf1wtFwuridVf87UVbm8kOautHSqsM9Qhx45MgMCBheQYzOwRB15O5WuP79gMf7azeXXnFvzKXv1cyaSuE6IUEgW3qNY9fLxSJ3BJoXZ1wa3x/5erdzVzxr6d9Jd8e1nn1SilRufpCiI1JENiGzeTxW6cfwf/hX8TP6F1lfH+rV/wbkYeoCyHWo2+8i1hLdx6/pmlxPr9uxttXsI6fZvxdv4GeG4FmFT03gv3A2ou++qU7VbRdU99OGUzP13b0uEKI/UHuBLYhLM9AKrd84zp5/Llb71v2vN1B2C/VT4UQu0PuBLZBLxTjYZ1uPebxD0o7VbSbPERdCNGWqJ6g32Wbu2vybzaPf1CPqpSHqAsh1pOYO4H2BKkfhuQzJn4YT5BW6t6W39M6fhr7gUc3Pc6/E21ZSztV1NTjISBT12VSWAjRkZg7gen5GkOLisL5JzBqcwTZcconH2Q6fc+2FkRtJatnK3V9tkMWfQkh1pKYO4Fw6llGXvgKeqNEZGXRGyVGXvgK4dSzA29LzfVJmcs/+pSpU3NlslYIMViJCQJjF79NqBnx2L2mxVk8msHYxW8PvC0yWSuE2CsSEwRSjXlCzSKMIiIgjCJCzSLVmB94WybGsrjNANeLSzW3K3ROjGUH3hYhRLIlJggYwwex9QBN0wjDKF44pQcYwwcH3haZrBVC7BWJGX+wTj9C+OQXSWkapFrpnFHQUzrnTpDJWiHEXpCYO4GtpnMKIcSNbNt3Ao7jfAT4XeAu4LeVUp9ZZ9+PAf8roAGPA59QSoVr7d9vO1WkTQgh9qt+3Ak8A3wI+Mv1dnIc52bg94CfBU61/vtIH44vhBBii7YdBJRSzymlngc2uqL/58BXlVIzrav/PwM+uN3jCyGE2LpBzgkcBy50fT8JHBvg8YUQQqyw4ZyA4zhPE3fgq5lQSgX9bdL6xsf3d+GzYrGw200YuCSeM8h5J8l+PucNg4BS6r4+HWsSONH1/XHg4mbfZG6uQhhGfWrSYBWLBWZmyrvdjIFK4jmDnHeS7PVz1nVt3YvnQa4T+E/AdxzH+T+AOeBjbDCZLIQQYmdte07AcZwPO45zCfgA8AeO41xyHOeu1mufchzn4wBKqXPAHwA/BF4GzgGPbff4Qgghtk6Lon0ztHISeFWGg/aXJJ4zyHknyV4/567hoJuB89e9PugGCSGE2DskCAghRIJJEBBCiASTICCEEAkmQUAIIRJMgoAQQiSYBAEhhEgwCQJCCJFgEgSEECLBJAgIIUSCSRAQQogEkyAghBAJJkFACCESTIKAEEIkmAQBIYRIMAkCQgiRYBIEhBAiwSQICCFEgkkQEEKIBJMgIIQQCSZBQAghEkyCgBBCJJi53TdwHOcjwO8CdwG/rZT6zBr7PQh8A3iptclVSv3Mdo8vhBBi67YdBIBngA8B/1sP+z6vlHpjH44phBCiD7YdBJRSzwE4jhNuvzlCCCEGqR93Aptxu+M4TwMe8G+UUl8Y8PGFEEJ02TAItDrt42u8PKGUCno81tPAMaXUkuM4NwPfdBxnSin1zR5/HoDx8fxmdt9zisXCbjdh4JJ4ziDnnST7+Zw3DAJKqfv6cSClVKnr61cdx/kq8ACwqSAwN1chDKN+NGngisUCMzPl3W7GQCXxnEHOO0n2+jnrurbuxfPAUkQdxznsOI7W+noMeJh4UlkIIcQu2XYQcBznw47jXAI+APyB4ziXHMe5q/XapxzH+Xhr1/cDzzmO8wzwHeCLSqmvbff4Qgghtk6Lon0ztHISeFWGg/aXJJ4zyHknyV4/567hoJuB89e9PugGCSGE2DskCAghRIJJEBBCiASTICCEEAkmQUAIIRJMgoAQQiSYBAEhhEgwCQJCCJFgEgSEECLBBl1KejsMiFe/7Wf7vf1bkcRzBjnvJNnL59zVNmO11/dT2Yi3At/d7UYIIcQ+9fPA91Zu3E9BwAbeBFwBen2GgRBCJJ0BHAZ+BLgrX9xPQUAIIUSfycSwEEIkmAQBIYRIMAkCQgiRYBIEhBAiwSQICCFEgkkQEEKIBJMgIIQQCbafykbcEBzH+SzwDuJFGxXgf1FKPbW7rdpZjuN8BPhd4C7gt5VSn9nlJu0Yx3FuB74AjANzwEeVUi/vbqt2luM4fwK8HzgJ3KuUem53WzQYjuOMA18EbiX+9/wK8C+UUjO72rBNkjuBwXuc+B/K64D/E/gPu9yeQXgG+BDwl7vdkAH4HPBZpdTtwGeBP93l9gzCV4G3ARd2uyEDFgH/l1LKUUqdBs4Cf7TLbdo0CQIDppT6a6WU1/r2B8BNjuPc0L8HpdRzSqnngXC327KTHMc5CNwHfKm16UvAfY7jFHevVTtPKfU9pdTF3W7HoCml5pVST3Rt+iFwYpeas2U3dOezD/zPwN8opW7ozjFBjgFTSqkAoPX/y63t4gbWupD7TeC/7HZbNkvmBPrMcZyngeNrvDzR7iAcx/kQ8N8T30bva72esxA3sP+HeI5v3813SRDoM6XUfRvt4zjOPwP+EHiHUmp651u1s3o554S4CBx1HMdQSgWO4xjAkdZ2cYNqTYyfAt6zH+/qZThowBzH+SfAvwbeqZQ6v8vNEX2klLpGPAn+4damDwM/3m/ZIqJ3juP8IXA/8MtKqevKNO8HUkp6wBzHmQGaQHfH8A6l1NwuNWnHOY7zYeCPgVHic68CD7cmi28ojuPcQZwiOgosEKeIqt1t1c5yHOfTwPuAQ8AsMKeUunt3W7XzHMe5G3gOeAmotza/qpT6Z7vXqs2TICCEEAkmw0FCCJFgEgSEECLBJAgIIUSCSRAQQogEkyAghBAJJkFACCESTIKAEEIkmAQBIYRIsP8fz8g8qSgr8LUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = pca.inverse_transform(X_pca)\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The light points are the original data, while the dark points are the projected version.\n",
    "This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n",
    "The fraction of variance that is cut out (proportional to the spread of points about the line formed in this figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n",
    "\n",
    "浅色的点代表原始数据，而深色的点是放射变换的得到的数据。上图清晰地表示了PCA降维的含义：沿着非重要维度上的信息都被移除了，只留下了具有高差异性维度上的数据。被移除的差异部分（按比例体现在图中深色线的数据点分布情况中）是降维操作中多少*信息*被丢弃了的粗略衡量。\n",
    "\n",
    "> This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the dimension of the data by 50%, the overall relationship between the data points are mostly preserved.\n",
    "\n",
    "降维后的数据集在某些情况下是原始数据点之间最重要关联的一个“足够好”的编码表达：虽然将数据的维度减少了一半，但是数据点之间的整体联系大部分被保留了下来。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA for visualization: Hand-written digits\n",
    "\n",
    "### 使用PCA进行可视化：手写数字\n",
    "\n",
    "> The usefulness of the dimensionality reduction may not be entirely apparent in only two dimensions, but becomes much more clear when looking at high-dimensional data.\n",
    "To see this, let's take a quick look at the application of PCA to the digits data we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb).\n",
    "\n",
    "当数据仅有两个维度时，降维的效果并不明显，但是在高纬度数据的情况下，这个操作的威力就体现出来了。为了展示这点，让我们将PCA应用在手写数字数据上，我们在[深入：决策树和随机森林](05.08-Random-Forests.ipynb)中已经看到过它的应用。\n",
    "\n",
    "> We start by loading the data:\n",
    "\n",
    "首先载入数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Recall that the data consists of 8×8 pixel images, meaning that they are 64-dimensional.\n",
    "To gain some intuition into the relationships between these points, we can use PCA to project them to a more manageable number of dimensions, say two:\n",
    "\n",
    "我们前面知道数据是由8x8像素的图像构成，这表示数据共有64个维度。要获得这些数据点之间的内在联系，我们可以使用PCA将它们投射到更容易管理的维度数量上，例如2："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 2)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(2)  # 将64维数据投射到2维上\n",
    "projected = pca.fit_transform(digits.data)\n",
    "print(digits.data.shape)\n",
    "print(projected.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> We can now plot the first two principal components of each point to learn about the data:\n",
    "\n",
    "然后我们就可以将数据的两个主成分绘制在下图中："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(projected[:, 0], projected[:, 1],\n",
    "            c=digits.target, edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('viridis', 10))\n",
    "plt.xlabel('component 1')\n",
    "plt.ylabel('component 2')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n",
    "Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits in two dimensions, and have done this in an unsupervised manner—that is, without reference to the labels.\n",
    "\n",
    "回忆一下这些成分的含义：完整的数据是64维的数据点组成的云，上图中的点是每个数据点投射到最大差异方向上的投射点。基本上来说，我们找到了通过最优的拉伸和旋转将64维数据展示在2维上的方式，并且采取的是一种无监督的手段，也就是没有任何的标签参考。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What do the components mean?\n",
    "\n",
    "### 成分的内在涵义\n",
    "\n",
    "> We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n",
    "This meaning can be understood in terms of combinations of basis vectors.\n",
    "For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n",
    "\n",
    "> $$\n",
    "x = [x_1, x_2, x_3 \\cdots x_{64}]\n",
    "$$\n",
    "\n",
    "让我们再继续深入介绍一下，提出问题，这个降维之后的结果究竟有什么意义。我们可以通过基本矢量的组合来理解它。例如训练集中的每张图像都是64个像素值的集合，我们把它称为$x$：\n",
    "\n",
    "$$\n",
    "x = [x_1, x_2, x_3 \\cdots x_{64}]\n",
    "$$\n",
    "\n",
    "> One way we can think about this is in terms of a pixel basis.\n",
    "That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n",
    "\n",
    "> $$\n",
    "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n",
    "$$\n",
    "\n",
    "用计算机图像基础术语来说的话，就是要构成一张图像，我们将上面的向量中的每个元素乘上它所代表的像素点，然后将这些结果加起来就能得到图像：\n",
    "\n",
    "$$\n",
    "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n",
    "$$\n",
    "\n",
    "> One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.\n",
    "For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!\n",
    "\n",
    "那么我们可以认为降维就是将除了需要保留的基础矢量外的部分全部移除。例如如果我们仅使用前面8个像素，我们就能得到8维的数据投射，但是结果并不能完整展示原图：因为我们丢弃了接近90%的像素。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](figures/05.09-digits-pixel-components.png)\n",
    "[附录中生成图像的代码](06.00-Figure-Code.ipynb#Digits-Pixel-Components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n",
    "Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n",
    "Were we to continue this sequence and use all 64 pixels, we would recover the original image.\n",
    "\n",
    "上图中第一行展示的是单独的像素点，第二行展示的是对应的像素点加入后对累计求和结果产生的影响。仅使用8个像素点基础成分时，我们只能构建64像素图像的一小部分。如果我们继续这个过程直到所有64个像素相加后，我们就能恢复原始图像。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some pre-defined contribution from each pixel, and write something like\n",
    "\n",
    "> $$\n",
    "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
    "$$\n",
    "\n",
    "但是逐个像素点的表示方式不是唯一的选择。我们可以使用其他的基本函数，其中包含着每个像素对图像的预设影响值，比方说写成\n",
    "\n",
    "$$\n",
    "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
    "$$\n",
    "\n",
    "> PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n",
    "The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n",
    "This figure shows a similar depiction of reconstructing this digit using the mean plus the first eight PCA basis functions:\n",
    "\n",
    "PCA可以想象成选择最优的基础函数，在这个函数当中只需要将头几项相加就能足够重建数据集的主要部分。主成分，我们数据的低维度表示，其实就是这个函数当中的头几项的系数。下图展示了使用平均值加上头8个PCA基本函数后重建的图像情况："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](figures/05.09-digits-pca-components.png)\n",
    "[附录中生成图像的代码](06.00-Figure-Code.ipynb#Digits-PCA-Components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean plus eight components!\n",
    "The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n",
    "This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel-basis of the input data.\n",
    "\n",
    "这个函数没有用到像素，PCA允许我们仅使用平均值加上8个成分就还原了原始图像中的显著特征。还原图中的每个像素都是我们二维例子中矢量叠加后的直接结果。PCA提供低维度数据表示方法的其实就是，它找到了一组基础函数能比输入数据的原始像素图方式更有效的表示图像。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the number of components\n",
    "\n",
    "### 选择成分的数量\n",
    "\n",
    "> A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n",
    "This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components:\n",
    "\n",
    "在实践中使用PCA的一个重要方面是能够估算需要多少个成分来描述数据。这可以通过查看*可解释方差比例*来决定："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(digits.data)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n",
    "For example, we see that with the digits the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n",
    "\n",
    "这条曲线量化了64维中头$N$个成分的可解释方差占比。例如我们看到使用头10个成分时可解释方差占比为75%，而成分数量需要到达50个左右时，这个比例才能接近100%。\n",
    "\n",
    "> Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance.  Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations.\n",
    "\n",
    "由上图我们也看到我们的二维投射损失了很多的信息（由可解释方差衡量）我们需要大概20个成分才能获得90%的可解释方差占比。将这个图应用在高维度的数据集上时，能帮助你理解不同观测角度情况下数据的冗余度情况。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA as Noise Filtering\n",
    "\n",
    "## 使用PCA去噪\n",
    "\n",
    "> PCA can also be used as a filtering approach for noisy data.\n",
    "The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n",
    "So if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n",
    "\n",
    "对于在数据中过滤掉噪音来说PCA也是一个好的方法。这其中的原理是：任何具有较大差异的成分相对来说都不会收到噪音的印象。因此如果你通过保留大部分主成分来重建数据集的话，应该能达到较好的去噪效果。\n",
    "\n",
    "> Let's see how this looks with the digits data.\n",
    "First we will plot several of the input noise-free data:\n",
    "\n",
    "让我们来看看它在手写数字数据集中的表现。首先绘制无噪音情况下的数字："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/8ssvyXYvGaeSTCULdebwjp9KzaljMjw8LLdVIzlWqqQPT506lWxXiy+adef1pCSxo+Sez2bp8Zt7HnpjVKVsVLLKGwudSOcq3n6pdKd6T9PXjNpUHSULhf/000/Jdi9dmTtG+WUHAACExmQHAACExmQHAACExmQHAACExmQHAACExmQHAACEVhQ996jFuVT80YupqQhtt1IRVi/2Oj8/n2z3Io1Nx9VV/FNFI73orhoPXg3L486Dg4NVo+fqMQgl1IKJ6hi2SZ2D3qMD2qzDuzaoiLl6FEDuooFtU+eU6kMvfq0i5t5inyo23TR13rb5CASPdx3LrcV7FEA3Ut/P586dy96W+o70xmjq2G/YoH+/4ZcdAAAQGpMdAAAQGpMdAAAQGpMdAAAQmneDcn/JBtUNQtu2bUu279y5U25r48aNJbvgWV5TUY2Kqt2rUd3E5t1o5ahSnzru27dvT7Z7N+mp2rds2SLfMzg4+Ke/f/HFF//745rrGxjQQ3vHjh3ytZTNmzfL19QxWYd+8ed1U+fg7t275XuW90UFa+5D77PVPr99+zbZ7o2Hyhq9xqjzxutDdUzWMXYbG6Nqn7Zu3VrzY1ZTpQ9VLSpssWnTppKPKVGlPjUWR0ZGsrelvie8MZr6juzr6/vfH1fU1Le4uKi2ddjMfvB3sed8bWb3l/w9Wo3U1/uW1hi9PrN4NUavz4wx2uui12e2skZ3svOFmR00sxdm9qnZ/Wpcv5l9ZWY/mtlvS9qj1Eh9vV2fWbrG6PWZxakxen1mjNFerzF6fWa6RneyAwAA0PO4QRkAAITm3bX3V/hpK0qN1Nfb9ZnxTwS9XmP0+swYo71eY/T6zJx/xvImOwct/k1L0Wqkvt63tMbo9ZnFqzF6fWaM0V4XvT6zxA3K3mTnRcknPH78ONl+/vz5ZLu35tGhQ4eS7WfOnMnfsd8tr6moRuXZs2fJ9sOHD2dv6/79+/I155hVqe+7777Lar969arc1rFjx0p2QVlzfSpua2Z27dq1ZPuDBw+S7WpMm+n45eXLl+V71Lj+wwvx58acPHlSvqbqyF2rbIkqY1Tt8yrHNkn1YeF1pkp9avyqur3xrs7Pffv25e/Y7xobo+oac+vWrext3bx5U762yvit0ofqO0/1lTfeSsa1o0p9ly5dSrar6+iJEyfkttbxna6sqMmb7BT9nPXhw4dk+/Pnz5Pt3rN0vBO40PKaqv5k9/Hjx2T7kydPqm1rFVXqU8/+UXW8e/eu5GNKrLm+z58/y42o+l6+fJlsf/r0qdyWesbQ+/fv5XtW8Un8uTGqbrPiceipMkbVPnsLwHZIlfrU+FXXUa9udU1eh8bGqKpD/Y+kZx1jt0ofvnr1KtmualzHNSNXlfpev36dbFdjtIHvc8+KmrhBGQAAhMZkBwAAhFb9GeoXLlxIts/Pz2e1m5nNzs4m28fHx+V79uzZI19r2sLCQmufncv72fv27dvJ9uPHjyfbvf5o6zlOXl88evQo2X7kyJGsdjOze/fuJdvVeeC9p2k3btxItnvHylsKpGmqn8zM5ubmstrV2DXz+7ct6t4Vdb0cHR2V22qzD3Op67fXR+p6dfbs2ez3dII6/0u+P7xrSdP9rs5PNUbPnTsnt6W+Q2p+n/PLDgAACI3JDgAACI3JDgAACI3JDgAACI3JDgAACI3JDgAACK0oeu7F3VRcfHJyMtnuRXT379+fs1tVedFsFbnzalHGxsaS7U1H6L1YojruKrrs9ZM6Vk33rbf93Nip9wRsta3Tp09nfUZN6vycmJhItk9PT8ttqQh0yVjP5Y3RkZGRZLsab90Yv/aixhcvXszaljo3zdp9HEcudd5455Oqr+0+z43Re9cltS3v8QxtPVJBPQbBe8yMumbVvI7yyw4AAAiNyQ4AAAiNyQ4AAAiNyQ4AAAiNyQ4AAAit+kKgikp1eLwUTNO8dIO3oFkEagE9lVDz7rLvpSSIGm/eIosq9dVmGkv1n0pEegsm9vX1Jdu9fq1VuzeulJKFQNviJT6VttKbJby0mbq+qnSRd6zUedv2MVGJRXXN8NJjJQukNk2d5yr16VHHijQWAADAGjHZAQAAoTHZAQAAoTHZAQAAoTHZAQAAoRWlsUruAFd303t3oKvkgZeUqrVmj5dQUfWrxNnMzIzclpdYaItKC6hjovrJrP31aXKo9Za8VIc6Jk3X7Z0DKsWk+nV8fDz78zuRNvNScOp6ompRSTSzsqRoDSVpU3W9UCk0s/aSaN4YzV37q0Qnrj1eSkydIyUpQ28NrLbkrmPmfdft3bs32e7Vnbu+Ir/sAACA0JjsAACA0JjsAACA0JjsAACA0JjsAACA0JjsAACA0KovBDo0NJRsV5FwL/apYn1tL/CmIm8l+9V2LSkq7qeipF60PgLvUQtqXJfEuXN40e/h4eFk+/fff59s78bHH5j554a6NqhaVLTVTD8+oOlzUz3qwKPi6iXj7fr16/K1Go8W8B4DkvuIEK++e/fuJdvbXIzXTO/Xw4cPk+1eVF/V4r2n23jnk3o0hDc/yK2dX3YAAEBoTHYAAEBoTHYAAEBoTHYAAEBoTHYAAEBo1dNY6q7x27dvZ28rd7G/tpWkN9QCfl5CpumUSO7xVekC7zXvM3IXeMul7vBX480bu95CgG1RCz+qdi/VMDExUWOXqlNJF9XuUeda0+eZt32V1CpZPFQpSf80TSXjZmdn5Xump6eT7Z1YCNT7DPVabtrVrDu/81Qd6hz0rqPqHPTGeyrRNzAwYLt27Ur+9/yyAwAAQmOyAwAAQmOyAwAAQmOyAwAAQmOyAwAAQmOyAwAAQqsePVfRwdyYmpmO4nUiUlhCLRg5NjYm36OOS5vRc9WHKjpYEvf1YojLt7dhwwbbsmVL9mcoudFzbyHQK1eu1NilVnmR16mpqc7tSAbVh+p8UgsNmvn92yTvOqbOj9zrq/c5vRRnHh0dle9pe8FPRe2XWgTVWxy1G2ssiZgr6jvNewxJ7vcgv+wAAIDQmOwAAIDQmOwAAIDQmOwAAIDQvBuU+4s2OJDe5I4dO5LtmzdvltsaHBws2QXP8pqKalRyazcz2717d7K9sPYq9ambgb06cnn9vmHDn+fgfX19//tjlfrU2imq7u3bt8tt9fdXHUJmf66p+sZTvH5tIAxQpQ9Vn6i+3bp1a8nHlKhS38aNG5Ptqq/UdcRMj+t13PTf2Bgt+Z5Yfr2ooEofqnMn9/pjVr3GnvmeqDRGzcysb3FxUf3Hh83sh9JP6lJfm9n9JX+PViP19b6lNUavzyxejdHrM2OM9rro9ZmtrNGd7HxhZgfN7IWZfWp2vxrXb2ZfmdmPZvbbkvYoNVJfb9dnlq4xen1mcWqMXp8ZY7TXa4xen5mu0Z3sAAAA9DxuUAYAAKF5Nyj/FX7ailIj9fV2fWb8E0Gv1xi9PjPGaK/XGL0+M+efsbzJzkGLf9NStBqpr/ctrTF6fWbxaoxenxljtNdFr88scYOyN9l5UfIJ58+fT7Y/ePAg2b5v3z65LbUOjPeeVSyvqajGZ8+eJdu/+eabZPuxY8fktlSNhdZcn6rBTNfx+PHjop1K8Y7J1atX1Utrru/WrVty+9euXUu2q74oqfvMmTPytVXilC/En9ftzp07yfZLly7J99y8eTPZruKza7DmPvSO+8mTJ5Pt3nFXVC0nTpzI3pZVusao8avWBDt06JDclhrXlfqwqL5//vOfyXZ1bf/222/ltmqum/eHKn2orjOKd81S54I6P83cMbHm+t6+fSu3r8aiqtv73lbnWsn5/IcVNXmTnaKfs169epVsV1+u27Ztk9v68OFDyS54ltdUVOPHjx+T7c+fP0+2qwUmG7Dm+lQNZrqOJ0+eFO1Uys8//1zytjXX9+uvv8qNqPrevXuXbC/pv8+fP2e/5w+fxJ/XTdXnTXy9cVJozX3onf9Pnz5Ntpf0VeVnCVW5xqjxq/pKXXfNGu/DovrUOaien7SO86lElT70Jgop6piY6Wvv+/fvsz7jD2uuzzvur1+/TrarffXOs9xjtQYrauIGZQAAEBqTHQAAEBqTHQAAEJp3z4507949+drMzEyyfXR0NNk+Pj4ut6Vee/TokXxPA2v5rKDqn5+fz2o3M9uzZ0+y/fTp05l7lcfbJ/XaqVOnku3/+te/5LaGhoaS7fv373f2bv0WFhbka6o+byzmUv1q1nzfqvtWpqamku1eX3h1NM27/+bNmzfJ9osXL2Z/jro2HTlyRL6n6eOSG1zwromqf73reI3zc3Z2Vr6mzkHV5zdu3JDbqhzyqMbb5xSvDrUtr9+98btWXg23b99Ott+9e7fatmr2Lb/sAACA0JjsAACA0JjsAACA0JjsAACA0JjsAACA0JjsAACA0Iqi5yVUtMyLcKr3tB1DHB4eTrarmHVJjU3Hk3/55Zfs96g46sjISPZ7mlYSDZ6cnEy2l0Sza8Q+S83NzSXbVdxXjcG2lTxGQvWhd11oK17vPR5BRevV4x+8a6Iav9571LpHOdT10KOue97+dGv0XB13VaPXH+pcaPp7wjsH1WMC1PVEPZbGzOz48eN5O1aAX3YAAEBoTHYAAEBoTHYAAEBoTHYAAEBoTHYAAEBo1RcCVUoSD+pO8L1792ZvqyZ15/iFCxeS7efOnZPb8hIZTfIWkFO8OpTr168n25tOEZS4cuVKst1LlXgJg7aopJ2qo2Sh2k4oSWOpPvSSLup61nSSsKQ+b9Hd3M85evRo9rZyeGNHJThLFnJVfdv2NUbVr467StqZtZeY9I6h+g5R32nT09NyWzXSf6vhlx0AABAakx0AABAakx0AABAakx0AABAakx0AABBa3+Lionptj5n9lHpBpY7M9N30zudI6m52L1mxyppEe81sYelHmKixU1SN3t33TkpkzfV5aSz12erYenfSq6SLWldlFVX6T+1T7npEZrovShKLf1ha4x4T9XnHT40pVZ+XNlN9XrKOzx+q9KEac+qzS9aOKkyIVKmvr68v2f7w4cNku5ccU695a0qtkmRa0xj1qPGrrkve9VCda945WGuMetfR8fHxZPuTJ0+S7SXfkYW67ntQ9Yd3fFdJii6vkV92AABAbEx2AABAaEx2AABAaEx2AABAaEx2AABAaEx2AABAaEULgdbkRWhVRK/pBfo6ScU/vXh/jUXhSqKqqq8KY+StUXFqFXNUkW2z9sZiSfQ8N+5rpuOz3vjsxKJ+6rxRNXr729Zip14fqscBqGtiycK+qm87QUWN1bnpPVJEnYPedbLWIqEln6H6anZ2Vm5LLT4dhepf7/EBuX3ILzsAACA0JjsAACA0JjsAACA0JjsAACA0JjsAACC0ojSWd2e8WghUJQ+8O6pVImGVRdxao+6y91IXKklw7tw5+Z6FhYU//X1gYMB27dq1+g6ukboDXiVg5ufn5bauX79eY5eyecdcpYVUssJbKLNWqiOXlyBS9R09ejTZ7i2S2a1JO5VcmZycTLZ7dXhJrSZ51zGVAFTnk5fGUtfrNq+jqv/UQqcHDhyQ21L1ef1a67z1vgvVeaXOXVW7WXtpLG9cqWOoUn5eH6rPmZiY0DuXiV92AABAaEx2AABAaEx2AABAaEx2AABAaEx2AABAaEx2AABAaNWj5yoiNzw8nGwfGxuT2/IWAWvT8uj3/6jj4sWEVSR2dHQ0c6/yqBrMdERZRbCnpqbkttqKZnuRSfV4BFWfNw67cVFaNQ5VtN5bEFIdk070qxcXP3XqVLJdxam98d6Nj7KYnp5OtqtHUnjR5E4szJrLu2akeDWomH7T11Az//xX43dmZibZ3tZjOjxefeo6oyL33qKpalve/CAXv+wAAIDQmOwAAIDQmOwAAIDQmOwAAIDQvBuU+0s2uH379mT7yMhIsn3Hjh1yWxs3bizZBc/ymopqHBhIH7bdu3cn23fu3Cm39eWXXybbt2zZsubP7+///zLWXJ+qwUz3ldqnDt7gueb6BgcH5UZy62tgHHr6xZ/XbdOmTcl2dTzMGjkma+7DDRv0/4upc03tr7etyqpcY1Qdqq/UddeskdrXPUa9a2LK58+f5Wtv376t8hlLVBmjud+F6rugAVXG6NatW5Ptap1G7ztt27ZtyaxAFJUAAACTSURBVPZ1jN0VNfUtLi6q//iwmf1Q+kld6mszu7/k79FqpL7et7TG6PWZxasxen1mjNFeF70+s5U1upOdL8zsoJm9MLNPze5X4/rN7Csz+9HMflvSHqVG6uvt+szSNUavzyxOjdHrM2OM9nqN0esz0zW6kx0AAICexw3KAAAgNCY7AAAgNCY7AAAgNCY7AAAgtP8DoC22XkcvhS0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                             gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))\n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Now lets add some random noise to create a noisy dataset, and re-plot it:\n",
    "\n",
    "下面我们增加一些随机噪音，来创建一个有噪音的数据集，并绘制数字："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c0YI/1ActaBYRKVKkiKqjcSLi9TILeK3mpy1WtRakomPhXKfSpUv77hOCyOB/+x2f8fHxqh4Vpd/uVt7ovf36kQWgXkPNv87yuUHnHOwb9+83McaDNX7DQM3vV3xe2QixsFalTJkyqm75TYXAM0b9ghYch/LB80Nuj1G/BHv8ZRHOcwYt+g/zGuZKfnFxcXrwMJ6vofwrw8BzElY1ViMRwS6deZPGIrIs4LVrOTK/vE9gjq7nJ+Jejq7nJ8IxmtdxPT8Rb47mZCe/iNQVkVQR8dqC5y0iRaSUiKwSkcC6OFdyZH55Oz8RPUfX8xNxJ0fX8xPhGM3rObqenwjO0ZzsEEIIIYTkebhAmRBCCCFOYy1Q/r/w05YrOTK/vJ2fCP9EkNdzdD0/EY7RvJ6j6/mJGH/GsiY7dcX9RUuu5cj88j6BObqen4h7ObqenwjHaF7H9fxElAXK1mQnFR149913YaeePXuq+ubNm1W9f//+MFaDBg1UHflv5YDgnGCOu3fvhkGQl9D06dNVHZVfi4gMHjxY1X/44QfYxyh3znF+U6dOhfEzMjJUPSUlRdUffPBBGAt5Oln+SZUqVUKHcpyfxR//+EdVnzZtmu9YU6ZMUfWDBw/CPr1797ZCpoJ/ZyMzMxMGWLZsmaqjUu6+ffvCWHv37lV1a63f/PnzPVpsbKw0adJEBFzDvXv3yqVLl7IdQD5JIvj+3LRpk6qjsnsRkV9++UXVUe4i3vunQIECWfeBmt/HH38s6enp2Q60bNkSxkdly+jZN2nSJBjLyiNMcjRGLc6fP6/qb775pqr/5S9/gbGQt5n13XLjjTcaZ5c7zxnktXfvvfeqOtrSRERkzpw5qj5r1izYp169euhQjvM7c+YMjH/06FFVR55c1jhEPmYnT56EfbQtR/Lly5e1rYEnJ2uyA3/OOnv2rNFNBz1Q0BeoiG1uFybBOcEcgx+8OQEZZVp7ISDTxmDTwByS4/zQuYrgBxG6Hsj4TQRPdsL5fMVHfhboxkLXwgJ9VuHcI9e4DP6dDWuygSaraLITTt4W6DO5hnoNL1265HlGHD9+HAZJTdWfzyiXcCY7Fsb9o+aXnp7uGRPh3OOnT59W9dy+hiHI0Ri1QOMXfbla+aFxEs51vUauPGfQOaNJQmJiou9Y1rPXIMf5XblyBQZBn284YxG9j3UNQ9w/noNcoEwIIYQQp+FkhxBCCCFOw8kOIYQQQpzGWrMD+d3vfgePWX42GuPHj4fH0GJD6z3QWhC/nivW308R27dvV/UnnnjCdyzkHZNbDB061Pd7o7+NV6hQAcZ69tlnVf3w4cOwz7Zt27K9joqKshYtq7z++uvwGPJhefjhh1Xd+rs1Whz52GOPwT59+vTxaEWKFIGLT8+dO+dZ44D8r0RE2rRpo+rovrF8adAiT7QwW0SkadOmOX7vLCpXruzR2rdvD9t36tRJ1e+44w5Vt7zY3n77bfPcNKz7R+O+++7zrDFA629EsJ/VSy+9pOqPP/64r/MRsdftrVq1yqPFxsbCz1dbW2F5ummLS8Plv/7rv1Tduq633HJLrry39bn/+OOPqo7uBWNBMcRPIUtUVBRcNI2wvNh69eql6miNKirsERFp166dqlsL0/3CX3YIIYQQ4jSc7BBCCCHEaTjZIYQQQojTcLJDCCGEEKfhZIcQQgghTsPJDiGEEEKcJqzSc6uMEzFw4EBVt0r3JkyYoOpWKbffEnORq/YBweXFpUqV8h3H8qdB3HfffaqeP39+2Cd4u/F8+fKZXlP79u3zlORb3l+oxHz9+vWq/uSTT8JYqPTc2uo7uGTS73YGIiKDBg3y3Qd5Sv35z3/2HcuyCLE8nzQuX77sKT1HPmwietmwheV11717d1W3xueLL77o0cK5hh07doTH0DVBJfHW5/UrbAVyzNdff+2xi7DGKNqGAH2ONWrUgLFQCXTBggVhH237AIvly5d7/NqQt6GISP369WEcDVRyLyJSrVo1VbcsVTQ7l4iICLMkfvfu3Z7naI8ePWB7VBaOfK4sj0E0RkeMGAH75AbdunWDx9C2FHPnzlX1PXv2wFioxHznzp2wz7fffuvREhMT4TOLv+wQQgghxGk42SGEEEKI03CyQwghhBCn4WSHEEIIIU7DyQ4hhBBCnCasaiyr0iQ5OVnVz58/7/t9PvzwQ1XPyMjwHcvCMjvT6NChg6ojg9SlS5fCWL1791b1xYsXwz7BppihKtCSk5M91WaWseb777+v6sFVYFns2rULxtq4caOq33zzzbBPbrB//354rGzZsqr+hz/8QdWPHTsGY6GKj2nTpsE+WuVBUlISfP/169d7Kl1uv/12GL9fv36qrlUviIikpqbCWD179lR1y7QwPT3do0VGRkpCQgLso2FVlY0aNcpXLKuCc+3ataquVexk4dcouECBAp5KqpkzZ8L26FmCxluVKlVgrBtuuEHV0bM6HBITEz0VeidPnoTtUfXN5MmTVX3kyJEwlmasK4KfPSIiR44c8WiW0amIbWSpge7Rr7/+WtWtqsC7775b1S0j0IYNGxpnlzM++OAD333GjBmj6tpnnsVbb72l6shsVERkwIABvs6Lv+wQQgghxGk42SGEEEKI03CyQwghhBCn4WSHEEIIIU7DyQ4hhBBCnCasaixrlX3Lli1V3a8fkIjI5s2bVb1u3bqwj+Y7Eh8fL82bN4d90tLSPNVK77zzDmw/e/ZseExj2LBh8FixYsVUHVVjiNieLxrbt2+XCxcuZNMaNWoE2992222qXrVqVVW/ePEijFW9enVVT0tLg33C8V4LBlVcieDxizyirMon5FXk9xpZpKSkeCqcvvnmG9geVY00a9ZM1ZF/mQiumjt9+jTsU7JkSXjMD9Z9vnfvXlVft26dqrdt2xbG2rp1q6rfeOONsE+wZ09UVJSUL18ettcqOL/44gvYHlVElihRQtXvvPNOGOvQoUOq/vTTT8M+qCoKcfbsWU/FoFXF2KZNG1VH3x8WqJrQ8prasGGD7/fRQH56IiILFixQ9eDPKYvOnTvDWH379lV169nrl7Nnz3qeW9azGF3fVq1aqbp1PyMftQMHDsA+o0ePhsc0+MsOIYQQQpyGkx1CCCGEOA0nO4QQQghxGk52CCGEEOI0nOwQQgghxGk42SGEEEKI04QsPd+yZYvHoOyWW26B7ZcvX67qyOhr8ODBMFbhwoVVferUqbCPVf6JOHPmjFy6dCmb9vjjj8P2qAzw+PHjqm6VvWumiSJ26Tkqd0acOnXKlxErKjH/7rvvVP3gwYMwFsrvp59+gn2Q6V1ugcbV22+/repWGTm6Fpb5q1Z2HxcXJ02bNlXbd+3a1aN9//33MH5wWXQWKO9NmzbBWNpWDiJ4W4hw+fzzz+XcuXPZtOuvvx62R6WqwVss5ARUxm6V1webB/u9J0VEWrduDY+h7S2QmeK4ceNgrKFDh6r6ihUrYB/NSDcyMlLKlCmjtteeVzt27IDxH330UVW3tlRAoK0OJk6cCPto90/+/PnNbSY0kMmqCDYj7tSpk6pb3zloawG0dYmI996Nj4+HJf8iV8dcsPlt+/btYfvSpUv7OifLMBqN0bFjx8I+LD0nhBBCCAmAkx1CCCGEOA0nO4QQQghxGk52CCGEEOI0nOwQQgghxGlCVmNFRER4Kg1SUlJg+3r16qn6kCFDVN1aTY5M74Krw34tWtUHqjwSEVg1U6lSJVVHFRQiIidOnFB1q5Jg48aN2V5HR0dLtWrVYPt69ep5jE5//PFH2B6ZoE6aNEnVa9WqBWMhU0rLJDAjIyPb64iICMmfPz9sP3ToUE8l3IwZM2D7tWvX+tKjo6NhLMS8efPgsRdeeMFXrH/84x+eCq7hw4fD9o0bN/YVP18+/H+edu3aqbplknn06FH1PYoWLQr7FClSRBISErJpllltjx49VP3DDz+EfRDIfHL8+PGwT3BFZqhqrOBqT5Gr5qGImjVrqnqTJk1U/d5774WxUJWPNa6150N8fDysxvruu+88961VbYbOCVXzWhWaKHerMler4Ap1DS9cuOCpzLTG9Ny5c3P83iJ29VqFChVU3bp3u3TpAo9pdO7c2ZNffHw8bI8MTdE5FSlSBMZ64403VN0ybJ0/f75Hi42NhZXM/GWHEEIIIU7DyQ4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUKWnhcvXtxTtmyV26GSUNTnn//8J4zVsWNHVa9SpQrsk1tYZa89e/ZU9T179qi6Vb5XqlQpVQ82ZAtkwYIF2V4nJSWZpecFCxb0aFaZI+KJJ55QdasMGZUCIzM8kauGg34YNGiQp7R3ypQpsP2TTz6p6miMamXDWaDyXcssd8uWLWqcypUrq+0HDBjg0d577z0YH92DaKxZRqfICBCZjYpcLf8MJtQ1veOOOzwaup9EsIll8LMqi4ULF5rvr2GZFD/99NPZXhcqVEhGjBgB21tl5n7ee9SoUapeo0YNX/FFrj43EJp5sVWajbbjQCCz4WeeeUbV0ZgWsbcJQWhjNBTa9hfW9gTIAPqvf/2rqi9ZsgTGQuMdGeKKiHz22WfZXsfFxZlbFMTFxcFjGq1atVL1RYsW+YojcnWeoRHOlgMI/rJDCCGEEKfhZIcQQgghTsPJDiGEEEKchpMdQgghhDiNtWouUsT23tBAi5wKFy6s6pbPlbWALkyCV0n6Wwl7DbSQFS3gK1euHIxVunRpX7FEvJ9LgQIFsv6Z4/yCfYgCQdcK+VMFvL8H5G+WmJgI+xio+WmLP61zKlu2rKqjvC3QAmXr89X6BOQQmGNY1w9x3XXXqbrlO4bex1pwqy1GDtByPEat90AeTeh5Es6CVItChQplex1QBJArzxgEGrvnz5/3Hcu6B7XnT4CWozEaDqiYA+X9G5Hja2h9hugZhBbjWuPdukcRwd/FAfdAroxR9Gy3vu8Q6DsVvUcO8OQUYVRiNBKR78N9p/9QGovIsoDXruXI/PI+gTm6np+Iezm6np8Ix2hex/X8RLw5mpOd/CJSV0RSReTyb3tevzmRIlJKRFaJyIUA3ZUcmV/ezk9Ez9H1/ETcydH1/EQ4RvN6jq7nJ4JzNCc7hBBCCCF5Hi5QJoQQQojTWAuU/y/8tOVKjswvb+cnwj8R5PUcXc9PhGM0r+foen4ixp+xrMlOXXF/0ZJrOTK/vE9gjq7nJ+Jejq7nJ8IxmtdxPT8RZYGyNdlJFRG5cOGC54BVBjd79mxVR35ESBcR6dKli6pb5WgpKSkeLTIyMssXKDXoUKqIyLp16+TixYvZDtStWxe+B2LOnDmqbvnyLF68WNU3bNjg+/0F5OeXZs2aqTryQxozZgw+oVT9FEaOHAn7rFq1KtvrmJgYqVmzpoiP/NLS0mD8lStXqjryNrK2ATh9+rSqb9y4EfYJUUaaGvzv1NRUuXw5+3+4UBl5ODz44IPw2A033KDqFStWhH2Qd9w1cnwN586dC4Mgr6C77rpL1U+ePAljIW83y4Mv2NMvISFB2rVrJwLyW7x4sWRkZGQ70LJlSxgf0b9/f1WfP38+7POPf/xD1Vu0aOH7/a/hGaMnTpzw+JKh7wIRkYcffljVkecbykFEJDk5WdUfffRR2CfEZ5/jMWp5DL722muqjsabdU7I+3DZsmWqLqL7zV17lqn5LViwwDNG77//fhgffXej5+vAgQNhLOQlaD17q1evDo+Jcs2syc6/n65+FjGfO3dO1fft26fqZ86cwSdw2f8vapZpo3h/orssInLx4kV1UucXlPuxY8dgn/379//q9w1Azc8vhw4dUnV0DS3T0lOnTvl+f+Na5Dg/ZAgpIp4bOosDBw6ounXDWV+iYXI5+N+XL18ONa5/FUeOHIHH0J4gxYoVC/ftcnwNrb1j0OeOrm16ejqMFfwfnZxgxFPzy8jICGsvnGDQswTdmyLh7cETAs8YvXLliuees/7DgUDPkoMHD8I+6Jr/irxzPEatfeLQtUJ7q1mxEJmZmb77iDFG0XeYxvHjx1Vd+8FBJLx70Hr2hsBzzbhAmRBCCCFOw8kOIYQQQpzG2menvIjs8Ruwfv36qo7+xh4O27dvh8esv7OLSAUR2RvwuryI7NoTTPcAABm5SURBVNm/f7/nzwTWT7C1atUKfZIBWOsb9uzRP2LrT4fBPzVGRERkbbOu5qf9OdD68xk632vrZjysW7cOxlqwYIGqo3VBIVDz27Jli+cnYPTnFxHJWr/lYfLkyaq+detWGGvChAmqPnHiRNinX79+8Jhkz7G8gHvQun5oa/1x48ap+lNPPQVjzZgxQ9Ufeugh2CcE6jU8efKk588g1k/qtWvXVvUOHTqourX+59lnn1X1QYMGwT516tTJ9rpUqVLyxRdfiID8YCAAGqPoz5noTwoiIqNHj1b1u+++G/Zp0qSJcXY5G6MWaK3J448/rurWGkp0bW+99VbY55FHHvFocXFxWWu+1Gs4ceJEz7ILa+3hX/7yF1VHfy4PHlOBoO8ja51P8J+AoqKistb6qfl9/fXXnj/9oftJix+Ke+65Bx778ssvVR3Z8eSA4Bz5yw4hhBBC3IaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaTjZIYQQQojTWDsoi4jI6tWrPTvaJiYmwvaoxLx79+6qjrYHF8GlbYUKFYJ9wkEr1Q22LAjkm2++UfUffvhB1VF5uUh4W8YnJCT4ah8ZGenRKlSo4Pt9165dq+pWmWrVqlVV/cSJE7BP8OcVExMDtxMX0bdf//TTT2F7VNaPbA7effddGAuVvaKSdBF9N9jk5GQZMmQI7BMMKi8XEVmzZo2qoxLzTp06wViFCxdWdVSSLiLSq1cveAwRERHhud/LlSsH2990002qjsqpX3/9dRgL2Xeg+1nk6nPRD0ePHvXsCG/tmFu+fHlV//HHH1Xd2qriWkm8B+u+1Xa7jYiI8PXssXbHRzucI4uJokWLwlhTpkxRdZS3iG7nEqrMWStXX758OWyPvqfQ9weyZhHB1hfWth/WM1ND+y5Cz5Jw2LVrFzyGnqPt27fPtffnLzuEEEIIcRpOdgghhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQpwlZjVWsWDGP+dw1MzFfoKorZBRpEWxWFshPP/3k0UJV82igagERbI6GjAu7dOkCY7Vr107V33nnHdjHrwnjmjVr5OLFi9m0evXqwfbIaHX37t2qblUEzJw5U9WtzyS4KiIqyh6m48aNk9OnT2fTbr/9dth+0aJFqo4+V8vwrk+fPqo+bdo02Oe3RjN+FcHXfNSoUTDWNWNED6+88grso1UfRkVFyfXXXw/7zJw502N2uG/fPtgeXZN58+apulVxtnLlSlUvU6YM7OOXmJgYzzMl+J4MBFVdoTGKKnxERFq3bq3qmZmZsM/f/vY3j1awYEF57LHHYB+tPWL69Omqjqr8WrRokeP3zQKZqYro1ZLx8fFSrVo1X+/RoEED38fQ83LMmDEw1s0336zqfr/XLFauXOmpvN68eTNsf/LkSVVHz5kdO3bAWL1791Z1qxpLq2qNjIyUkiVLqu35yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUJWY61bt85TZWT5sPjlnnvugcfQSmzLs6Zr166/+pxEcGWViMixY8dUPT4+XtVnzZoFYx0+fFjVrWoivxQoUMDjw2P5xqAKnJ9//lnVS5QoAWMNHz48B2eYneAqlVDVWEOHDvUVX/PFERE5deqUqmveW6H6/NYsXboUHkOeR8gvzKqwQfdn8+bNYR+r6goxcOBAj/bWW2/B9t9++62q79y5U9U///xzGAtVj0yaNAn2+dOf/gSPaSQnJ3s0VM1i8dVXX6n6HXfcAfugqraMjAzYp27duh4tNjYWtn///ffl7Nmz2TSrQgyNxf79+6u69QzVzlUEe/mJiHTs2BEeQ2RkZHi++1CFqgi+R8ePH6/qMTExMNahQ4dUfcOGDbBPsLdcRESE6Wupfec0btwYtke5o2re4KruQAoUKKDqVjUY8sdD8JcdQgghhDgNJzuEEEIIcRpOdgghhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQpwlZet6qVSuPtn//fti+aNGiqv7AAw+o+scffwxj9ejRQ9Vz0/xM5Gp5W3Bpds2aNWF7VP6JDFJTUlJgrNq1a6u6H8O9UOzZs8dTZnr//ffD9gsXLlT1Zs2aqfrbb78NY3Xr1k3Vx44dC/tUqVIFHssNqlev7qs9KvsUsUtPEZqJZlJSkgwYMCDHMdLT0+ExzYhTBG83oBnqZfH999+rulUKjIxIIyMjYR9tO4v8+fPD9qi8ddmyZar+3HPPwVjFixdXdau8fMmSJdle58+fX+rXrw/bHzlyxPO5hNpSQeP48eOqPnjwYNgHbWNhGZ1+8MEHvs5LK+W2thX55JNPVH3ixImqXqhQIRjr1VdfVXU0DsNlw4YNHqNM6zNEZs7IrNYyHO7evbuq+71OfpkyZQo81rRpU1+xtm7dCo+NHj1a1dE2GiL6FiL58uWTYsWKqe35yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUKWA2gVFMGVS4EEmzhmgYzfrKqcP/7xj6puVceEw/z58+X06dPZtBEjRsD2HTp0UPXU1FRVRxUtIthc87PPPoN9Bg0aBI9pXHfddZ7rcuTIEdgeVV0hkJmpiMiwYcNUPV++3JtnL1iwwFNtZpl3ooqdYOO8LG644QYYa8WKFar+0ksvwT5a9Q8ywhO5+vkGV5aULVsWtkfVCGjc3HnnnTBWjRo14DGEVXWFWLhwoecaWma1yKh33bp1MD7i9ddfV3Vk+CtiV4loaGa58+fPh+2RGS8au5mZmTAWMqS0Kpz8olXOVapUyXecuLg4VbcqgCdMmOD7fTST0JiYGNNc0q85c0JCgqqjXB599FEY680331T1OXPmwD6oAtoPWjV2Fqj6eNu2bapuGcMic1RUfSiimwcXK1ZMJk+erLbnLzuEEEIIcRpOdgghhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQp+FkhxBCCCFO49+JTkSqVq0Kjx09elTVGzdurOozZ86EsRYtWqTqV65cgX20ctW4uDjTtGzIkCEezTJ43Lx5s6qjcuCPPvoIxkJlv1Z5ebDxZoECBVQjviy0csodO3bA9siIExnVWYaG6Lysz1czhbSwDAc1GjVqpOqo9NPKD5XwI3PJ3OLs2bPwGCp5Rfj9/ETsa2QZGiIaNmzoiWmVUyPz0jfeeEPVLcNGa5uC3CIlJUUuXbqUTbv33nthe7SNxZYtW1S9Tp06MNaXX36p6jNmzIB9Vq9e7dFiYmLgVgTadiTR0dEwPkIzdxTB5fMiuEzfIpxrvmLFCo8RqFVe//DDD6t6ly5dVH3nzp0wFirnjo+Ph338smvXLs91jI2N9R3n5ZdfVvXk5GTYB5XJp6WlwT5+TVD5yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jTWAmX/BjcGpUqVUnVrMSVaHGV572jeKgFxgjvCQNaiVOTfghZOI88lEd0zJxTBPkoBi9RyJT+0mBMtPE1KSvIdK9jrKYfkOD+L66+/XtULFiyo6iVLloSxctPj6xqRwf/WxrvmRRQuyOMmt9/nGuo11MaWtfgyMTFR1dG9Zl3DXEbNz69fGHouomtlLYhHnwl6jolcXYwcTMCCY88YzS2QX5c1Ri1fuTBRr6H2mVjXFY1fdD3C+c4JZwGxgPy097fOCVGkSBFVt74nUH7aZ55DPBcmwqiqaCQi2MEyb9JYRAKd9FzLkfnlfQJzdD0/EfdydD0/EY7RvI7r+Yl4czQnO/lFpK6IpIpIWP8N/w8iUkRKicgqEQmsHXQlR+aXt/MT0XN0PT8Rd3J0PT8RjtG8nqPr+YngHM3JDiGEEEJInocLlAkhhBDiNNbqo/8LP225kiPzy9v5ifBPBHk9R9fzE+EYzes5up6fiPFnLGuyU1fcX7TkWo7ML+8TmKPr+Ym4l6Pr+YlwjOZ1XM9PRFmgbE12dHMWwd5QItjD47nnnlN1y/ti79698FiYBOeUKiKydu1auXjxYrYDpUuXhkGQP82TTz6p6i+++CKMddttt6n6sWPHYJ/gcsfo6OgsPys1Pw3Lh6VZs2aqXrt2bVW3fJqOHz+u6mPHjoV97r//fnRIzU8r+T906BCMj7yxvvrqK1Vfvnw5jHXzzTerev369WGfEKSCf2fj/PnzMMDkyZNVHZ3ruHHjYKzPPvtM1a2S17lz53q0uLi4rHGlXsPg+09EZMGCBfA9kI/Zjz/+qOpt2rSBsZ544glV79atG+xjoOY3ffp0z7NuyZIlMEiDBg1U/dtvv1V1y3eoZ8+eqm59Jm+++aZHK1CggHTt2lUkh2N0/vz5MP6kSZNU/e6771b1zp07w1iaL5fIVa8nxMmTJz1afHy8NG/eXMTHc9Ri/Pjxql6xYkVVnz59Ooy1Zs0aVV+8eDHsU758eXQoV/JD12TlypWqbm0lgbwz0bMsB3hysiY78OcsNLhERM6dO6fqBw4cUPXTp08bp5DrBOd0WeTqgzbY4C3YtC+QjIwMVd+/f7+qW19MaL8Z7eGfhbG3g5qfhnUN9+3bp+porxJrwoqMMtE4CUGO87P28UH5oc/Eys8yqwyTy+Df2bAKC9A9hcahNTEMp4DBGu/i4xpacdA1RNc9JSUFxkpPT4fHwkDNLy0tTc6cOZPtwOHDh2EQdA3RtbLGYTj3mjXmJYdjFD0nRXDuwZ/Rv9/EuJ/Rs/pXfCY5HqMWKBf03tZ4QOPd+p4yyJX80Pmic7X21LP+cx8mnpy4QJkQQgghTsPJDiGEEEKchpMdQgghhDhNSOOLpUuXev72+dJLL8H2yLMG8d1338Fj1apVU3Vj4ZV88803vt5f5OoC2+C/L1sL/rZu3arq6O/cXbp08R2rTp06sE9u8M477/jug3yu0KJCEZG2bduqOvKhCodRo0bJiRMnsmnW378Rd955p6qHs67M+hv06tWrPVpsbKw0adIkx/FnzZoFjz3//POqjq6T9b5orcu1BfEqDRs29GihvKE0D5wdO3bA9miBNPJQ6tGjB4yFFsv2798f9glei5YvXz4pVqwYbN+3b1/P+qff//73sL31jPMLWv/XunVr2AcVW/gB3fsiIgMHDlT11157TdVbtWoFY916662qbi2ItbzEENOnT/cUY1jehshLsHv37qq+cOFCGGvw4MGqbj3HrSKQnLJs2TJ47Pvv9QKuIUOGqPq9994LY6HF5GgdrIi+xjIqKgp6j/GXHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaTjZIYQQQojTcLJDCCGEEKcJWXpeq1Ytj/dQ7969YfuHHnpI1ZFnVpEiRWCspk2bqrpV4hkO6H0QqCwd+XhY3lioBNMqQ/RLWlqa5xpavjiVK1dWdbQ1ueWzhSwYrNLs4LESFxdnli326tXL8z5vvfUWbI9AY1cri86iatWqql60aFHY55r/To7561//6il/R+XlIiLvvfeeqqNyfKtEFY0FC82rDJXhZrFmzRqPZUu/fv1g+woVKqg68o6ynlmVKlVSdeQLJmKXVWukp6d7LA9+/vlnXzEsLFsPNH6XLl0K+1il3hraNbc885BlwieffKLq1lYcaPsSa0uMcOjTp4+v9lOnTlV19Lmg8nIR7BdoPRdnzJiR7XVCQoJ07NgRtt+3b5/nGR+8pUcgyD4IPdutMbV7925VL1u2LOzjF/6yQwghhBCn4WSHEEIIIU7DyQ4hhBBCnIaTHUIIIYQ4DSc7hBBCCHGakNVYx44d86zQRivpLVDVyrx582Cf4OqMLKxKlE8//dSjxcfHm6vWd+zY4anmOXnyJGzfqFEjVZ8+fbqqI2M0EWxcuGrVKtinbt268JhGXFycR5s2bRps/9///d+qjlbmHz9+HMZCBm+zZ8+GffxSsWJFj2Z9fqiS5tSpU6o+c+ZMGOvDDz9Udese0araIiIiJCkpSW1foEABtdoFgap86tevr+o33XQTjHXgwAFVX7x4MezTokULj5Yvn/3/qvj4eImOjs6mWWanqHoD3YNW5dP777+v6g0aNIB9/JKWluZ5xiQkJMD2hQoVUvVwDHwfeOABVbeqsbTndVRUFDQo1a6vZfaLDDSDK4iysK4FqqazqsG0Z6LI1Rz9cObMGXjshx9+UHVkMIsMQkVEOnTooOponIjg7ylEsWLFPFV9f/jDH2B7ZJyMPttOnTrBWNozXETk4MGDsE96erpHi4qKgrH4yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUIuPddWuq9btw62R1VXqLKiS5cuMFbLli1VvXTp0rDPsGHDPFooX54qVaqYx4PZunWrqjdp0kTVf/rpJxircOHCqm5VK/mtxgquchGx/ZmeeeYZVUdVD0OHDoWxrEqt3ELz/rGqCHr16qXqhw4dUvVvvvkGxgr2O8rCqrSZOHGiR0tMTJSePXuq7TWPKKsKBFWVvf3226pu+YgNGjRI1SdMmODr/UNVY1WrVs2jWVVi6B586qmnVL1mzZowVkpKinluGsGVopGRkeZzKSEhwVOFZ3nyoWuI7tuNGzfCWIsWLVJ16/MNxxMtGKsicfv27aq+fv16Vbe8sVCFmOUXplVrxsTEmONkzZo1cvHiRY+GCPazC8WIESPgserVq6s68oIT8XoyFi5cWP785z/D9pMmTfKcMxo7IiL79+9XdeRnhSpzRfTKKhHbB9O63zT4yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaTjZIYQQQojT+HM9u8ayZcvgMVRSeMstt6j66tWrfb//mDFj4LHIyEjf8TSssskvv/xS1bdt26bqd999N4yFjO8ee+wx2Ce4pDAcgksoA0EGfqh08IMPPoCxkFncwoULYR/r89LQSkyR+aEF2gbAKptG493aOkArH/ZrQIhKNUVwiTkqq127di2M9cgjj6j6XXfdBftY5ap+sD53ZATaunVrVb/xxhthrJdeeknVX3vtNdjHKtvW0Ax/P/roI9gePS+RGa+1fcBtt92m6qicWUR/lkVFRcHtJzZs2OB5pljl4mg7DlR6HmyiGggao2iLCRGRv/3tbx4t1PYItWvX9mjJycmw/aZNm1QdlcofO3YMxnr33XdVHW1XISJSsmTJbK+1LUgCadSokWdLBWRmKiLSsGFDVUfbcaCxI4K3oJk7dy7s0759e3hMg7/sEEIIIcRpONkhhBBCiNNwskMIIYQQp+FkhxBCCCFOw8kOIYQQQpwmrGqs+Ph4331QNYRmAJgFWh2fWxVXWRw8eNCzgvzKlSuwfa1atVS9b9++qm5VT6EV7eGYEyJ27NjhqWbo0aOH7ziWKRvi+eefV3VkGCsiMm/evGyv4+LioMmqiG70iowURUQGDx6s6qiKyeLZZ5/13Sc3WL58OTymGYeKiCxZssT3+0yaNEnVp06dCvv8/PPPHi0mJsas/tF477334LFp06apeps2bVQ9Li4Oxjp//ryv8xIR2bNnT7bXUVFRcv3118P227Zt89yDnTt3hu1RdUrXrl1VPTMzE8YqV66cqnfo0AH20UxxreduUlKSx+jUqi7SjDhFRBo3bqzqVnUqMsO0rnmhQoXgMT+MHDkSHpszZ46qowrcgwcPwljW8xLh936bM2eOp9qvbdu2sP3LL7+s6mXKlFF1dM1FRP7+97+rumXm6hf+skMIIYQQp+FkhxBCCCFOw8kOIYQQQpyGkx1CCCGEOA0nO4QQQghxGk52CCGEEOI0IUvPlyxZ4ilrRGZ7IrgsXSsPFhEZPXo0jIXKli1WrFjh0WJiYlQTtyxQqRwCGbmlpqaqumV62a1bN1VHpo0iIvv27cv2OjIyUjUazKJKlSoe7emnn4btly5dCo9pvPHGG77ah6JFixa/OoaVAyoxL1q0qKpbRpkZGRmqbpW9PvPMMx4tOTlZhg8fDvsEY43ZKVOmqPrYsWNVHd2bIriU2ypJPXLkiEcLZUJ45MgRz/YPZ8+ehe0XL16s6sgk2G8ZbiiCS5dDmUhaW2xonDlzRtWRSe+IESNgrHC2jChdurSv9lp5+969e2H7YcOGqTr6nLTtDLJA+Wnl878GrQzaMvxFZsSvvvqqqk+YMAHG2rFjh6rXq1cP9gk2W42JiYEGsyJXr2HwuEYmsiLYjPjBBx9U9a1bt8JYaLzv3LkT9jl8+LBHy58/v9StW1dtz192CCGEEOI0nOwQQgghxGk42SGEEEKI03CyQwghhBCnsRYoR4pcXfATjKZlgRbQIX+W5ORk4xT8ExMTY2nB5i65arKFcixSpIjvPtYCwWCPmoDXOc7P8oYpWbKkqqNzTUxMhLGiosKyX0PkOL+EhAQYBOVRuHBh/U0NTyBrcS9CG/NJSUn/frvAt0YxrHsQ4ffeFBEpXry4qlsLcrXFyAHjQL2GWjxrXKFzRjmG4+dnEXy+AeMgV54xaFyF8xwNGFu5RY7GqHXvly1bVtVLlSql6tYYRc9XVDyQA3LlGqKF08iLLTY2FsaynmeI4O/CgPtSzU+736xnHzondK2s8YCKQ6w+2jPQ+K6XCMNoq5GIfA/fKW/SWESWBbx2LUfml/cJzNH1/ETcy9H1/EQ4RvM6rucn4s3RnOzkF5G6IpIqIpdRozxCpIiUEpFVInIhQHclR+aXt/MT0XN0PT8Rd3J0PT8RjtG8nqPr+YngHM3JDiGEEEJInocLlAkhhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQp/l/fHNFLVqJczMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "noisy = np.random.normal(digits.data, 4)\n",
    "plot_digits(noisy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> It's clear by eye that the images are noisy, and contain spurious pixels.\n",
    "Let's train a PCA on the noisy data, requesting that the projection preserve 50% of the variance:\n",
    "\n",
    "肉眼可见图像变得多了一些随机噪音像素点。然后在带噪音的数据上使用PCA，保留50%的可解释方差："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.50).fit(noisy)\n",
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Here 50% of the variance amounts to 12 principal components.\n",
    "Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits:\n",
    "\n",
    "上面的输出告诉我们，只需要使用12个主成分就可以保留50%的可解释方差。然后我们进行仿射变换，先转换成主成分，再逆转换回来，就可以重建过滤掉噪音后的数字："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(noisy)\n",
    "filtered = pca.inverse_transform(components)\n",
    "plot_digits(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional representation, which will automatically serve to filter out random noise in the inputs.\n",
    "\n",
    "这个保存信号或过滤噪音的特性使得PCA在特征选择过程中非常有用，例如，与其在非常高维度数据上训练一个分类器，你倒不如在数据的低维度表示中去进行训练，这样做的好处是哪些数据中的随机噪音已经被过滤掉了。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Eigenfaces\n",
    "\n",
    "## 例子：特征脸谱\n",
    "\n",
    "> Earlier we explored an example of using a PCA projection as a feature selector for facial recognition with a support vector machine (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n",
    "Here we will take a look back and explore a bit more of what went into that.\n",
    "Recall that we were using the Labeled Faces in the Wild dataset made available through Scikit-Learn:\n",
    "\n",
    "前面章节我们探索了使用支持向量机（参见[深入：支持向量机](05.07-Support-Vector-Machines.ipynb)）来进行人脸识别，那里我们采用PCA作为特征选择器。下面我们回顾一下并且更深入的探索一下。回想之前我们使用的Scikit-Learn提供的标注后的Wild数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n",
      " 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n",
      "(1348, 62, 47)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_lfw_people\n",
    "faces = fetch_lfw_people(min_faces_per_person=60)\n",
    "print(faces.target_names)\n",
    "print(faces.images.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Let's take a look at the principal axes that span this dataset.\n",
    "Because this is a large dataset, we will use ``RandomizedPCA``—it contains a randomized method to approximate the first $N$ principal components much more quickly than the standard ``PCA`` estimator, and thus is very useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n",
    "We will take a look at the first 150 components:\n",
    "\n",
    "让我们首先查看一下这个数据集的主要成分。因为这是一个较大的数据集，我们会使用`RandomizedPCA`，这个方法会使用一个随机的方法来估算数据集的头$N$个主成分，它比标准的`PCA`评估器要快的多，因此在高维度数据中很有用（本数据集中维度接近3000）。我们看一下头150个主要成分：\n",
    "\n",
    "译者注：RandomizedPCA在新版Scikit-Learn中已经过时，统一采用PCA，只是需要传递一个`svd_solver='randomized'`参数即可，下面代码做了调整。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=150, random_state=None,\n",
       "    svd_solver='randomized', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA as RandomizedPCA\n",
    "pca = RandomizedPCA(150, svd_solver='randomized')\n",
    "pca.fit(faces.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as \"eigenvectors,\"\n",
    "so these types of images are often called \"eigenfaces\").\n",
    "As you can see in this figure, they are as creepy as they sound:\n",
    "\n",
    "在这个情况下，我们会发现将这些提取出主成分的图像可视化会得到很有趣的结果（这些成分在技术上被成为“特征向量”，因此这些图像经常被称为“特征脸谱”）。正如你下面看到的，这些图像看起来很怪异："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 24 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n",
    "                         subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                         gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n",
    "Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving:\n",
    "\n",
    "这些结果很有意思，它们为我们提供了图像内在的差异性：例如，左上角开始的几张特征脸谱看起来像是被不同角度的光照之下的结果，而后面的主要向量则似乎选择了不同的脸部特征，例如眼睛、鼻子和嘴唇等。然后我们看一下这些成分的可解释方差的比例曲线，得到脸部信息保留比例的大概印象："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> We see that these 150 components account for just over 90% of the variance.\n",
    "That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n",
    "To make this more concrete, we can compare the input images with the images reconstructed from these 150 components:\n",
    "\n",
    "于是我们发现150个成分已经保留了超过90%的差异。这让我们确信使用这150个主成分，就可以还原大部分数据的特征了。更具体的来说，我们可以将原始图像和通过150个成分还原的图像进行比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 计算主成分和还原的图像\n",
    "pca = RandomizedPCA(150).fit(faces.data)\n",
    "components = pca.transform(faces.data)\n",
    "projected = pca.inverse_transform(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制结果\n",
    "fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                       gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "for i in range(10):\n",
    "    ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n",
    "    ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n",
    "    \n",
    "ax[0, 0].set_ylabel('full-dim\\ninput')\n",
    "ax[1, 0].set_ylabel('150-dim\\nreconstruction');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n",
    "This visualization makes clear why the PCA feature selection used in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) was so successful: although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in the image.\n",
    "What this means is that our classification algorithm needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which depending on the particular algorithm we choose, can lead to a much more efficient classification.\n",
    "\n",
    "第一行是原始图像，第二行是通过约3000个初始特征中选出的150个主要特征还原得到的图像。上面的结果很清晰的解释了为什么主成分分析选择的特征在[深入：支持向量机](05.07-Support-Vector-Machines.ipynb)当中应用得如此成功：虽然它将特征的数量减少到初始数量的20%左右，但是它投射得到的图像包含了足够的信息，我们可以通过肉眼就分辨出每张图的个体。这意味着我们的分类算法只需要在150维的数据上进行训练，而不是在3000维数据上进行，这会带来更高性能的分类。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis Summary\n",
    "\n",
    "## 主成分分析总结\n",
    "\n",
    "> In this section we have discussed the use of principal component analysis for dimensionality reduction, for visualization of high-dimensional data, for noise filtering, and for feature selection within high-dimensional data.\n",
    "Because of the versatility and interpretability of PCA, it has been shown to be effective in a wide variety of contexts and disciplines.\n",
    "Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationship between points (as we did with the digits), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n",
    "Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n",
    "\n",
    "本节中我们讨论了使用主成分分析进行降维、对高维数据可视化、去噪和高维数据特征选择的方法。因为PCA算法的可解释性和灵活性，它在大范围的情景和方法中展现了有效性。当面对一个高位数据集时，作者倾向于首先使用PCA来将数据点的关联关系可视化出来（正如我们在手写数字中做的那样），然后试图找到数据中的最主要的可解释方差（正如我们在特征脸谱中做的那样），还有用来理解数据的固有维度量（通过绘制可解释方差比率）。当然PCA也不太适用于非常高维度的数据集，但是它提供了一个直接和有效的探视高维度数据内部特征的途径。\n",
    "\n",
    "> PCA's main weakness is that it tends to be highly affected by outliers in the data.\n",
    "For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n",
    "Scikit-Learn contains a couple interesting variants on PCA, including ``RandomizedPCA`` and ``SparsePCA``, both also in the ``sklearn.decomposition`` submodule.\n",
    "``RandomizedPCA``, which we saw earlier, uses a non-deterministic method to quickly approximate the first few principal components in very high-dimensional data, while ``SparsePCA`` introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components.\n",
    "\n",
    "PCA的主要缺点在于它容易受到数据中离群值的影响。正因为此，很多更加健壮的PCA变种被开发出来，其中很多都致力于迭代丢弃哪些初始成分很少影响到的数据点。Scikit-Learn也包含了一些PCA的有趣的变种，包括`RandomizedPCA`和`SparsePCA`，它们也位于`sklearn.decomposition`包中。`RandomizedPCA`我们上面用来在高维数据中快速的近似的找到主要成分，而`SparsePCA`通过引入一个正则项（参见[深入：线性回归](05.06-Linear-Regression.ipynb)）来强制让成分变得稀疏。\n",
    "\n",
    "> In the following sections, we will look at other unsupervised learning methods that build on some of the ideas of PCA.\n",
    "\n",
    "在下面章节中，我们还会看到其他的一些构建在PCA理论基础上的无监督学习的方法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n",
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